ON the SPATIAL VERSIONS of the ZAKHAROV and DYSTHE MODELS

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Abstract

Spatial evolution of nonlinear deep-water wave groups is studied experimentally and numerically. Spatial two-dimensional version of the Zakharov equation describing evolution of deep-water gravity waves is used to derive two 4th order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented. The experimental results for wave groups with initial narrow spectrum are compared with the computations based on the unidirectional Zakharov equation and the Dysthe model. The very good agreement between the computational results based on both models with the experiments prompted an attempt to perform simulations for a wider initial spectral width, that formally violate the assumptions adopted in the derivation of the Dysthe model. The accuracy of the results based on the Dysthe model is checked against the solutions of the Zakharov equation, which is free of restrictions on the spectral width. Conclusions regarding the domain of validity of the Dysthe model are drawn.

Original languageEnglish
Title of host publicationProceedings of the 28th International Conference on Coastal Engineering 2002
Subtitle of host publicationSolving Coastal Conundrums, ICCE 2002
EditorsJane McKee Smith
PublisherAmerican Society of Civil Engineers (ASCE)
Pages1143-1154
Number of pages12
ISBN (Electronic)9812382380, 9789812382382
DOIs
StatePublished - 2003
Event28th International Conference on Coastal Engineering, ICCE 2002 - Cardiff, Wales, United Kingdom
Duration: 7 Jul 200212 Jul 2002

Publication series

NameProceedings of the Coastal Engineering Conference
Volume2003-January
ISSN (Print)0161-3782

Conference

Conference28th International Conference on Coastal Engineering, ICCE 2002
Country/TerritoryUnited Kingdom
CityCardiff, Wales
Period7/07/0212/07/02

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